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function in trigonometry

...concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin),
cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

work of Euler

Euler’s analytic approach is illustrated by his introduction of the sine and
cosine functions. Trigonometry tables had existed since antiquity, and the relations between sines and
cosines were commonly used in mathematical astronomy. In the early calculus mathematicians had derived in their study of periodic mechanical phenomena the differential equation